University of Birmingham > Talks@bham > Theoretical computer science seminar > Adjunctions and Actions of Co/Cartesian Categories

## Adjunctions and Actions of Co/Cartesian CategoriesAdd to your list(s) Download to your calendar using vCal - Francisco Lobo (University of Manchester)
- Friday 30 September 2016, 11:00-12:00
- Computer Science, The Sloman Lounge (UG).
If you have a question about this talk, please contact Paul Taylor. When a category is cartesian it is possible to consider actions of such a monoidal structure in the sense of Janelidze and Kelly (2001). If F:X->A is adjoint to U:A->X, the latter will not only be cartesian but also give a linear transformation between canonical actions of X. In the dual situation where X and A are cocartesian, the adjoint F will not only be cocartesian but also a linear transformation of actions of A. If X and A are bicartesian, it turns out that there exists a module theoretic characterization of when F is adjoint to U. This fact is the generalization to categories of a result Jónsson and Tarski (1951) obtained for Galois connections between boolean operators, and which is fundamental in the axiomatization of relation algebras. This talk is part of the Theoretical computer science seminar series. ## This talk is included in these lists:- Computer Science Departmental Series
- Computer Science Distinguished Seminars
- Computer Science, The Sloman Lounge (UG)
- Theoretical computer science seminar
- computer sience
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